if z1=-2+i, z2=3-i then value of z1×z2
Answers
If z1 = 2 + 5i, z2 = 3 - i find (a) z1 · z2 (b) z1 × z2 (c) z2 · z1 (d) z2 × z1 (e) acute angle between z1 & z2 , (f) Projection of z1 on z2
Answer:
Answer
Correct option is
B
1,−17,1,17,cos
−1
290
1
,
10
1
(a) z
1
⋅z
2
=a
1
a
2
+b
1
b
2
=(2)(3)+(5)(−1)=1
(b) z
1
×z
2
=a
1
b
2
−a
2
b
1
=(2)(−1)−(3)(5)=−17
(c) z
2
⋅z
1
=a
1
a
2
+b
1
b
2
=(2)(3)+(5)(−1)=1
(d) z
2
×z
1
=a
2
b
1
−a
1
b
2
=(3)(5)−(2)(−1)=17
(e) Let angle between z
1
and z
2
be θ
then z
1
⋅z
2
=∣z
1
∣∣z
2
∣cosθ
1=
(4+25)
(9+1)
cosθ
cosθ=
290
1
θ=cos
−1
(
290
1
)
(f) Projection of z
1
on z
2
=
∣z
2
∣
z
1
⋅z
2
=
a
2
2
+b
2
2
a
1
a
2
+b
1
b
2
=
10
1